Magnetorotational Instability around a Rotating Black Hole

The magnetorotational instability(MRI) in the Kerr spacetime is studied on a 3+1 viewpoint. The Maxwell's equations are expressed in a circularly orbiting observer's frame that co-rotates with matter in Keplerian orbits. There exist large proper growth rates in MRI around a rapidly rotating black hole. The large "centrifugal force" and the rapid variations of magnetic fields are caused by the rotation of spacetime geometry. As the result, in the extreme Kerr case the maximum proper growth rate at $r=r_{ms}$ becomes about twelve times as large as that in Schwartzshield case.